Why does linking materials between objects seem to have no effect?
It has 'changed the color' ... to Material.04.

You could have been linking materials between objects with completely different topologies.. the editor has no way of knowing which materials to assign to which faces. So by default, it will assign the material in transferred-slot-0 to all faces.

If you switch the order of the material slots in the first cube, (using the up/down arrows at the bottom right of the list,) when you link the materials to the other cubes, they will turn blue. All over.